Charge Transport in Solid-State Dye-Sensitized Solar Cells - The

Article pubs.acs.org/JPCC

Charge Transport in Solid-State Dye-Sensitized Solar Cells Alessio Gagliardi,* Desiree Gentilini, and Aldo Di Carlo* CHOSE, Center For Hybrid and Organic Solar Energy, Department of Electrical Engineering, University of Rome Tor Vergata, Rome, Italy ABSTRACT: A new model based on detailed numerical simulations is proposed to show how the doping of the electron transport material in solid-state dye-sensitized solar cells (ss-DSCs) changes the nature of carrier transport in the device. Differently from standard DSCs, where charge transport is fundamentally diffusive, in n-doped ss-DSCs, it becomes drift driven. The relevance of the internal electric field of the cell casts light on the influence of trap states within ss-DSCs.

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solid-state hole conductors6 (see Figure 1). Until now, none of these alternative solutions have shown the same efficiency as

INTRODUCTION Dye-sensitized solar cells (DSCs) are an interesting alternative to conventional photovoltaic devices.1 They belong to hybrid cells due to their intermixing of organic/inorganic materials and organic or organo-metallic molecules. Conventional DSCs are made of a mesoporous semiconducting layer, usually TiO2. This semiconductor film is covered by a monolayer of dye molecules in order to turn the material photoactive in the visible range. The dye monolayer is in direct contact with a liquid electrolyte. The light-to-electricity conversion follows several steps: the incoming photon excites the dye, which transfers an electron to the semiconductor having the characteristics of an electron conductor; at the same time, the ionized dye is regenerated by the electrolyte, which behaves as hole conductor. Finally, the redox couple in the electrolyte is regenerated at the cathode by a platinum layer that acts as catalyst. A DSC is a majority carrier device where recombination can occur at the interface between liquid electrolyte and semiconductor material only. Despite the recombination rate is much smaller than the analogue losses parameter in conventional solar devices based on p−n junctions,2 the interface area between the mesoporous material and the electrolyte is so large that recombination remains a big issue. Several engineering problems plague DSCs, in particular the integrity of the liquid electrolyte. In fact, contamination from the external atmosphere or escaping of the electrolyte from microcracks within the sealing material deteriorate the efficiency of the cell in time, shortening the device lifespan. Finding a good sealing for DSCs is still an open problem.3 Moreover, the most suitable electrolyte for photoelectrochemical cells uses, as a redox couple, iodide/triiodide ions. They are corrosive if they come in contact with metallic fingers used to collect electrons in the external circuit.4 For this reason, it has been proposed to substitute the liquid electrolyte with gel5 or © XXXX American Chemical Society

Figure 1. Scheme of a ss-DSC. On the left the mesoporous material made of nanoparticles covered by dyes, red dots (shown in the Generation inset). The porous material surrounded by the hole transport material (HTM) (orange) with which recombination occurs (second inset Recombination). The anode represented by the transparent conductive oxide (TCO) and the cathode for holes collection. (color online)

using liquid electrolyte. This is related to several reasons: for gel electrolyte, the main drawback is the slow mobility of ions with severe effects over the maximum current. For solid-state hole conductors, instead, two main problems are usually addressed: a faster recombination kinetic at the interface and a worse pore Received: June 9, 2012 Revised: October 22, 2012

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filling of the hole conductor within the TiO2 nanoparticle network.7 However, recent studies have shown that, in the case of P3HT as a hole conductor, the pore filling does not seem to be the real bottleneck for the cell efficiency.8 This suggests that maybe this is not the main issue in such systems. In order to improve solid-state DSC (ss-DSC) efficiency, ionic additives are inserted in the organic materials during cell fabrication. Theoretical investigations on ss-DSCs are generally focused on the coordination effect of these ionic additives9 and on mobility of lithium ions. The gap between the modeling of the device and the many experimental measurements is broad, and many questions are still open. In this work, we simulate an operating ss-DSC using a drift diffusion model coupled to the Poisson equation. We explore the possibility that additives inserted into the blend can dope the electron conductor material, assuming that the ionic additives chemisorb at the interface between electron and hole conductor and get ionized giving an electron to the TiO2. This increases the free and trapped electrons concentration and leaves a background of fixed positive charges. It is clear that, under this assumption, the ionic additives cannot move into the organic matrix as free ions and then cannot screen the internal electric field. We will show that, in this case, the transport is mainly drift driven and the effects of the electric field result to be critical for explaining the transport behavior. If the bonding between ions and TiO2 particles does not occur and the ionic additives are completely dissociated and free to move, the functioning of the device could be diffusion driven (as suggested in ref 10). From an electrostatic point of view, this is exactly what happens in a standard DSC. Using a liquid electrolyte with a high density of charged ions results in a efficient screening effect of the macroscopic electric field inside the cell.11

where k 0 is the recombination rate constant, β the recombination exponent,16,17 and Nc the effective density of states in the conduction band for the TiO2. The electron density in the recombination includes electrons in the conduction band only, but recombination occurring via surface states is included by the recombination exponent.18,19 For the generation, we assume a Beer−Lambert law for light absorption: G=

nt = Nt e−aEf / kT

∇(ε0εr ∇ϕ) = −q(nc + ND+ − n I− − n I3− − ne +

⎞ ⎟⎟ ⎠

∑ ntk) k

(1)

(5)

The effective dielectric constant εr is calculated using a Maxwell−Garnett model25 to describe the effect of porosity for the two mixed materials. At the anode, we assume no ionic current (▽ϕI− = ∇ϕI3− = ▽ϕc = 0) and a rate equation for electron collection. For a high collection rate (νe > 108 cm s−1), the boundary condition reduces to an ideal contact:

where the index α stands for iodide, triiodide, electrons, and cations, μ is the mobility, n the density, ϕ the electrochemical potential, and Γ is a stoichiometric coefficient equal to 1 for electrons, 0.5 for triiodide, −1.5 for iodide, and 0 for a cation. For charge densities, we use the Boltzmann distribution. G is the photoelectron generation due to illumination, and R is the recombination. The mesoporous TiO2 is treated as an effective material that contains both ionic species and electrons. The main recombination process that occurs at the electrolyte/semiconductor interface is treated as an effective volume recombination rate, density dependent: n I3−n I−n I̅ 3− Nc ⎛ β n I3− ⎜n − ne̅ β β⎜ e n I̅ 3− Nc ⎝ n I−

(4)

nt is the trapped electron density, Ef the electron Fermi energy, Nt is the effective density of localized states, and a is the parameter describing the energy depth of trap distribution. k is the Boltzmann constant, and T is the absolute temperature. It is assumed that the conduction band and trapped electrons are in thermodynamic equilibrium and then they are controlled by the same Fermi energy. The presence of traps is widely treated in the multiple trapping model20,21 (MTM) and implies to deal with a density dependent diffusion coefficient. In the MTM, it is assumed that all the electrons (trapped and free electrons) propagate with a density-dependent electron mobility.18,22 The current equation for a pure diffusive transport within the MTM in the steady state is equivalent to a pure conduction band transport with a constant mobility.23,24 This model is commonly used for standard DSCs where the screening induced by the ionic species in the electrolyte, having a greater concentration than photogenerated electrons, efficiently screen out any long-range electric field. Our model explicitly includes drift current, and we distinguish between trapped and free electrons; therefore, the electron mobility is considered constant. The Poisson equation takes into account both ionized dyes (N+D) and different trap sources (nkt ) with the proper charge sign:

MODEL The differential equations of the drift diffusion model are solved using a finite element method, within the TiberCAD software tool.12 The model for DSCs has been discussed in different works;13−15 we only briefly summarize it here. We will focus on the particular assumptions introduced in the previous section concerning ss-DSCs. The two following subsections refer to standard (liquid electrolyte) DSCs and ss-DSCs, respectively. Standard DSC. For a standard DSC with liquid hole conductor, we use drift−diffusion equations for all charged species (iodide, triiodide, cation ions, and electrons):

R = k0

(3)

where α is the dye absorption spectrum and Φ is the light source spectrum. We used a standard 1 Sun 1.5 a.m. spectrum as light source, and N719 absorption spectrum as the dye molecule. Experimentally, it is known that the electronic transport is affected by an exponential band tail of trap states below the conduction band edge:20

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∇·(μα nα∇φα) = Γα(G − R )

∫ α(λ)Φ(λ)e−α(λ)xdλ

Ef − Eredox − eη = eV

(6)

where Ef and Eredox are the Fermi energy level of electrons in TiO2 and the redox energy level of electrolyte, respectively, η is the overpotential at the cathode, and V is the external voltage. At the cathode, we assume no electron and cation currents (▽ϕe = ▽ϕc = 0) and a Butler−Volmer equation for ionic species:

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j = j0 [eqγη / kT − e−qγη / kT ]

where C0 is a recombination constant, n and p are the electron and hole densities, respectively, and ni is the equilibrium concentration. The value of C0 used in the model (2 × 10−8 cm s−1) has been chosen in order to obtain open circuit voltages consistent with experimental IV characteristics. The open circuit voltage is in fact dominated by generation and recombination; therefore, by fixing the generation, we get information about the value of the recombination parameter. In order to rule out a possible effect of the chosen value for C0 in the results discussed in the present work, different values (between 10−9 cm s−1 and 10−7 cm s−1) have been tested. We did not observe modifications in the conclusions we present in this work. In ss-DSCs,19 recombination is assisted by surface states at the interface between TiO2 and organic material. We have approximated this aspect assuming a direct recombination between electrons and holes. In order to improve cell performances, ionic additives are always introduced into the organic hole conductor during the preparation of ss-DSCs.32 The effect of ionic additives can be various.33 If they dissociate in free ions and move into the organic matrix, it is possible that they behave exactly as ionic species in standard DSCs. Their effect is mainly to screen the electric field resulting in a diffusion driven device. Another concurring effect is related to hole conductor doping.34 In case additives do not dissociated in free ions, the screening is reduced, and the internal electric field becomes relevant. We focus on this second scenario making a further assumption that the additives chemisorb at the TiO2 interface and ionize giving an electron to the TiO2 (see Figure 2). This process is

(7)

where j0 is the exchange current (0.1 A/cm2), η is the contact overpotential, and γ is the symmetry factor (equal to 0.5). Finally, we assume ion conservation for cation and iodine ions, considering that no process in the cell creates or destroys these ions in the system. Parameters for the cell are enlisted in Table 1. Table 1. Parameters for a Standard DSC with Liquid Electrolyte symbol

value

unit

electron mobility iodide diffusion triiodide diffusion

parameter

μe DI− DI3−

5 10−5 10−5

cm2/(V s) cm2/s cm2/s

iodide eq. conc triiodide eq. conc

n ̅I − n̅I3−

0.45 0.05

mol/L mol/L

cation eq. conc recombination constant recombination exponent trap density trap exponent porosity electron collection rate (anode) exchange current density (cathode)

n ̅c k0 β Nt a ε νe j0

0.5 103 0.7 1020 0.3 0.5 108 0.1

mol/L s−1 cm−3

cm/s A/cm2

Solid-State DSC. Since the two types of cells share the structure of the photoanode, we adopt for the electron conductor the same model in terms of trap distribution (eq 4) and the mobility model as described in the previous section. The blend, formed by the intermixing of TiO2 and the hole conductor, is described by an effective material with a constant model for electron mobility and a field-dependent mobility for holes (Poole−Frenkel model): μ h = μ0h e

F F0

(8)

μh0

where and F0 are the mobility and exponent constants, respectively, and F is the local electric field intensity. The electric field dependency for organic material mobility depends very much on the type of material. For several hole conductors, like P3HT, density dependency is more important than field dependency.27 However, in this paper, we discuss a SpiroOMeTAD hole conductor, where the Poole−Frenkel model for the mobility has been found correct28 with a poor density dependency.29,30 For the generation, we assume the same model of the standard DSC and the same light source and molecular dye, N719 (eq 3). Recombination in ss-DSCs is different to standard DSCs with liquid electrolyte. For the latter, in fact, the recombination is fundamentally a minority carrier recombination due to the huge difference in average density between electrons (in the range of 1017 cm−3) and ionic species (>1020 cm−3) in the electrolyte. In ss-DSCs, the average density for electrons and holes is in the same order of magnitude; then, we expect that recombination is more similar to bimolecular recombination found in fully organic solar cells:31 R = C0(np − ni 2)

Figure 2. Effect of additives in case they do not dissociate. (a) The additive molecule approaches the interface between TiO2 and holeconductor material. (b) The additive chemisorbs at the surface giving an electron to the porous semiconductor. This electron can go into a free state of TiO2 or be trapped in a trap state leaving a fixed positive charge. (color online)

equivalent to doping the electron transport material. The injected electron can occupy a free or a trap state. In this scenario, besides the presence of an internal electric field, an enhancement of electron conductivity occurs due to the doping effect. The performances of this drift driven cell are very sensitive to the concentration of additives, D+. The energy of the positive ionized ions D+ is assumed to have a fixed energy 0.2 eV below the conduction band edge. Under the assumption that the additives are always ionized at room temperature, this parameter is immaterial for the results of the simulation. On the contrary, their density is of paramount importance for the performances of the cell. The simulations are performed by varying the doping concentration and fixing the density of trap states in the exponential band tail.

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The anode and cathode are modeled as Schottky barriers, representing the interfaces between the electron and hole conductors and the metal. In order to extract information on the transport characteristics of the active layer of the cell, we reduce the influence of these barriers considering an energy height of 0.1 eV and simulating good collection rates at the contacts(νe = 1010 cm s−1, and νh = 1010 cm s−1 for electrons and holes, respectively). In the absence of doping, ionic additives, and trap states, that is, with an ideal ss-DSC, the different injection energy barriers between the blend and the contacts produce a long-range electric field that favors charge collection. This electric field is then screened by the presence of trapped electrons lowering the cell efficiency. We will show that, with doping the TiO2, it is possible to restore this electric field and that a drift driven ssDSC achieves a reasonable efficiency. For the ss-DSC we have considered a blend between titanium dioxide and Spiro-OMeTAD as the hole conductor. Spiro-OMeTAD is a typical choice due to the nice pore filling obtained with this material. The parametrization is enlisted in Table 2 where the references for different values, not previously discussed, are reported.

Figure 3. Different ss-DSC IV characteristics with different doping concentrations of the TiO2 (D+). For comparison, an IV characteristic of a conventional DSC is plotted. (color online)

asymmetry giving to the current a diffusion behavior. The effect of insertion/adsorption of positive lithium ions in TiO2, in standard DSCs, causes mainly a positive shift of the conduction band edge.37 Different cases for the internal electric field intensity in a ssDSC are shown in Figure 4 where conduction and valence bands and electrochemical potentials for electrons and holes at Jsc are plotted. The first figure (Figure 4, left) refers to an ideal cell with neither trap states nor ionic additives. At Jsc, both the electronic and the hole bands are bent meaning that the internal electric field, induced by the asymmetric barriers of the contacts, drives charge carriers toward the contacts. When the exponential band of trap states is added Figure 4, middle, the effect is to screen the electric field creating a space charge that stops electrons to be collected. As mentioned, free electrons and trapped electrons are in thermodynamic equilibrium; they share the same Fermi energy. The Fermi energy is controlled by trapped electrons due to their higher concentration compared to free electrons in the conduction band. The effect of doping additives (Figure 4, right) is to pin the Fermi energy closer to the conduction band. This has two main consequences: it increases the electron conductivity and generates a higher current. Moreover, the positive background of ionized additives screens trapped electrons restoring the electric field in the system and enhances the drift component of the current. A higher concentration of dopants shifts the Fermi energy closer to the conduction band edge increasing not only the concentration of free electrons but also of trapped electrons. In particular, the trap density of states grows quickly close to the conduction band edge due to its exponential shape. This means that it exists an optimal concentration for doping additives related to the density of trap states below the conduction band edge. For a higher concentration of dopants, the increase in the space charge of trapped electrons overcomes the advantages due to the increase in the TiO2 conductivity. In Figure 3, different IVs for several concentrations of D+ are shown. The cell performances increase enhancing the amount of doping up to 1018 cm−3 and then reduce drastically for higher values of D+. The control over the population of trapped electrons by doping with ionic additives is shown in Figure 5 for two different concentrations (1017 and 1018 cm−3) at Jsc. It can be

Table 2. Parameters for a ss-DSC parameter

symbol

electron mobility hole mobility electric field exponent recombination constant trap density trap exponent doping density porosity electron collection rate (anode) hole collection rate (cathode)

μe μh0 F0 C0 Nt a D+ ε νe νh

value 5 10−4, ref 35 2 × 106 2 × 10−8 1020 0.3 1017−1018 0.7, ref 36 1010 1010

unit 2

cm /(V s) cm2/(V s) V/cm cm3/s cm−3 cm−3 cm/s cm/s

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RESULTS AND DISCUSSION In order to obtain reliable results from the simulations, a careful parametrization is needed. We have already defined a set of parameter ranges for conventional DSCs, extracted comparing our numerical results with experimental measurements; nevertheless, for a complete description of the parametrization of the model, we reference to our work.23 The geometry of the cell is made of 10 μm of mesoporous material and 50 μm of bulk electrolyte. The parameters used in the simulation for conventional DSCs are enlisted in Table 1. For ss-DSCs, the parameters are reported in Table 2. We underline that, for the TiO2, we use the same values as for a standard DSC. The geometry of the cell is 3 μm of blend and 200 nm of pure hole conductor. The IV characteristics for a typical illumination of 1 Sun are shown in Figure 3. By comparison a standard DSC is also shown. Conventional DSCs show a far better short circuit current (Jsc) and worse open circuit voltage (Voc) compared to ssDSCs. We get 14.09 mA/cm2, with respect to a maximum of 6.15 mA/cm2 for the best performing ss-DSC and 754 mV with respect to 809 mV. As pointed out previously, in standard DSCs, the presence of the ionic species in the electrolyte, with high concentrations (more than 1020 cm−3), efficiently screens out macroscopic electric field inside the cell due to contact D

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Figure 4. Conduction (Ec) and valence (Ev) bands and electron (ϕe) and hole (ϕh) electrochemical potentials at short-circuit conditions. The bands and potentials shown refer to an ideal (left) ss-DSC with no trap states and ionic additives, a different device with trap states and a density of 5 × 1017 cm−3 positive charges (D+) (middle) and a final cell with trap states and a density of 1018 cm−3 positive charges (D+) (right). (color online)

Figure 5. (left) Internal densities (hole, electrons, and trapped electrons), at Jsc, for a ss-DSC with a concentration of ionic additives of 1017 cm−3. (right) Same plots for a different concentration of ionic additives (1018 cm−3). (color online)

noticed that, for a high concentration of doping (1018 cm−3), a gradient in the hole concentration appears, meaning that, beside a drift current, there is also a diffusion current contribution. However, this diffusion contribution is generally lower than the drift component, and it opposes to charge collection, which is fulfilled by the drift component. Moreover, due to the electric field dependency of the hole mobility, even the diffusion component is partially field dependent. Internal currents for holes and electrons for the two D+ concentrations are shown in Figure 6, left. To make a comparison, current contributions for different charge carriers are also plotted for a standard DSC at Jsc (Figure 6, right). It is important to stress that the efficiency of the cell is related to the maximum region where an electric field is present; beyond this thickness, the diffusion component neutralizes the drift component and the electrochemical

potentials of electrons and holes start to become flat. The effect is clearly shown in Figure 7 where the internal electric field within the ss-DSC for two different concentrations of doping, D+, (1017 and 1018 cm−3) are plotted. In the first case, the electric field is absent in most of the blend, and the current reduces strongly. On the contrary, in the second case, the better balance between positive ionized ions and trapped electrons allows a strong electric field in the system and a consequent high current. The correlation between the current intensity and the region where an electric field is present and not screened by the space charge induced by trapped electrons suggests that there is also an optimal blend thickness. Beyond this thickness, despite a better light harvesting, we expect a reduction in the cell efficiency. E

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Figure 6. (left) Internal currents (hole and electrons), at Jsc, for a ss-DSC with two different concentrations of doping (1017−1018 cm−3). (right) The current distribution of the different charged species (electrons and ions) for a standard DSC at Jsc. (color online)

Figure 7. (left) Internal electric field, at Jsc, for a ss-DSC with two different concentrations of doping (D+). (right) Internal electron current and drift component. (color online)

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This limiting effect on cell efficiency is clarified in Figure 8 where IV characteristics and efficiency curve are plotted for different ss-DSCs with varying blend thickness. For small blends (1 μm), the IV shows bad performances due to a poor light harvesting whereas, the efficiency increases up to 2 μm where the efficiency is the largest (1.94%) despite a lower Jsc compared to other thicknesses. The lower short-circuit current is anyway compensated by the better fill factor. The best cell performances are obtained for a blend thickness that avoids the region where the electrochemical potentials are flat. In our case (Figure 8), this means an optimal thickness of 2 μm. A further increase in blend thickness improves the maximum current thanks to a better light harvesting but does not improve the overall efficiency that starts to decrease due to a worse fill factor.

CONCLUSION

In this work, we use a drift−diffusion model for DSCs to explore differences that can occur in the electrical transport of standard and ss-DSCs. The presence of trap states creates a space charge that forbids an efficient collection of electrons. This bottleneck can be overcome by screening trapped electrons; for example, this is what happens in a standard DSC thanks to the high concentration of ions in the electrolyte. It is possible that a similar screening occurs also in ss-DSCs after the adding of ionic salts. In case ionic additives do not dissociate and get fixed at the TiO2/hole-conductor material interface, injecting an electron into the TiO2, the situation is completely different. Additives cannot freely move into the organic matrix screening the internal electric field, which becomes the main driving force for charge collection. Moreover, the electron transfer into the TiO2 F

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Figure 8. (left) IV characteristics for ss-DSCs, varying the blend thickness; the IV for the cell with a blend thickness of 3 μm is plot in red. (right) Efficiency plot (the red star refers to the 3 μm thick cell). (color online) (3) Sastrawan, R.; Beier, J.; Belledin, U.; Hemming, S.; Hinsch, A.; Kern, R.; Vetter, C.; Petrat, F.; Prodi-Schwab, A.; Lechner, P.; Hoffmann, W. Sol. Energy Mater. Sol. Cells 2006, 90, 1680−1691. (4) Okada, K.; Matsui, H.; Kawashima, T.; Ezure, T.; Tanabe, N. J. Photochem. Photobiol., A 2004, 164, 193. (5) Papageorgiou, N.; Athanassov, Y.; Armand, M.; Bonhote, P.; Pettersson, H.; Azam, A.; Graetzel, M. J. Electrochem. Soc. 1996, 143, 3099−3108. (6) Bach, U.; Lupo, D.; Comte, P.; Moser, J. E.; Weissortel, F.; Salbeck, J.; Spreitzer, H.; Graetzel, M. Nature 1998, 395, 583−585. (7) Snaith, H. J.; Moule, A. J.; Klein, C.; Meerholz, K.; Friend, R. H.; Graetzel, M. Nano Lett. 2007, 7, 3372. (8) Abrusci, A.; Ding, I.-K.; Al-Hashimi, M.; Segal-Peretz, T.; McGehee, M. D.; Heeney, M.; Freyd, G. L.; Snaith, H. J. Energy Environ. Sci. 2011, 4, 3051. (9) Kuang, D.; Klein, C.; Snaith, H. J.; Moser, J.-E.; Humphry-Baker, R.; Comte, P.; Zakeeruddin, S. M.; Graetzel, M. Nano Lett. 2006, 6, 769. (10) Krulger, J.; Plass, R.; Graetzel, M.; Cameron, P. J.; Peter, L. M. J. Phys. Chem. B 2003, 107, 7536−7539. (11) Soedergren, S.; Hagfeldt, A.; Olsson, J.; Lindquist, S. J. Phys. Chem. 1994, 98, 5552. (12) der Maur, M. A.; Penazzi, G.; Romano, G.; Sacconi, F.; Pecchia, A.; Carlo, A. D. IEEE Trans. Electron Devices 2011, 58, 1425. (13) Gagliardi, A.; der Maur, M. A.; Carlo, A. D. IEEE J. Quantum Electron. 2011, 47, 1214. (14) Gagliardi, A.; Mastroianni, S.; Gentilini, D.; Giordano, F.; Reale, A.; Brown, T.; Carlo, A. D. IEEE J. Sel. Top. Quantum Electron. 2010, 16, 1611. (15) Gagliardi, A.; der Maur, M. A.; Gentilini, D.; Carlo, A. D. J. Comput. Electron. 2011, 10, 424. (16) Villanueva-Cab, J.; Oskam, G.; Anta, J. A. Sol. Energy Mater. Sol. Cells 2010, 94, 45. (17) Bisquert, J.; Mora-Sero, I. J. Phys. Chem. Lett. 2010, 1, 450−456. (18) Kopidakis, N.; Schiff, E. A.; Park, N.-G.; van de Lagemaat, J.; Frank, A. J. J. Phys. Chem. B 2000, 104, 3930−3936. (19) Bisquert, J.; Fabregat-Santiago, F.; Mora-Sero, I.; GarciaBelmonte, G.; Gimenez, S. J. Phys. Chem. C 2009, 113, 17278−17290. (20) Frank, A. J.; Kopidakis, N.; van de Lagemaat, J. Coord. Chem. Rev. 2004, 248, 1165. (21) Anta, J. A.; Mora-Sero, I.; Dittrich, T.; Bisquert, J. Phys. Chem. Chem. Phys. 2008, 10, 4478−4485. (22) Cao, F.; Oskam, G.; Meyer, G. J.; Searson, P. C. J. Phys. Chem. 1996, 100, 17021−17027.

is equivalent to a doping that enhances electron conductivity and improves charge efficiency by overcoming the space charge effect induced by trapped electrons. A balance between electron trap density and doping concentration is needed in order to obtain the best performances. Therefore, the nature of the additives introduced in the fabrication process can tune charge transport from diffusion to drift driven. The drift current in ss-DSCs poses also limits to the effective thickness of the active region. Depending on the intensity of the long-range electric field present in the cell, which is determined by the nature of the blend/contacts interface, an optimum thickness can be evaluated. Beyond this optimal thickness, we get a better Jsc current, thanks to an improved light harvesting, but a worse fill factor and an overall worse efficiency. Our theoretical work can help further improvements for this promising technology. If carriers are drift driven, then a larger energy difference between the electron conductor conduction band and hole conductor valence band could increase the intensity of the internal electric field or the active thickness of the cell, improving the performances of the device.

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AUTHOR INFORMATION

Corresponding Author

*Phone: +39 (0) 672597367; fax: +39 (0) 672597939; e-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are very grateful to Annamaria Petrozza for fruitful discussions. We acknowledge Polo Solare Organico−Regione Lazio and PRIN2008 project for funds.

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REFERENCES

(1) Regan, B. O.; Graetzel, M. Nature 1991, 353, 737−740. (2) Kalyanasundaram, K.; Graetzel, M. Coord. Chem. Rev. 1998, 77, 347. G

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